UNIFORMLY SUPERCONVERGENT APPROXIMATIONS FOR LINEAR 2-POINT BOUNDARY-VALUE-PROBLEMS

A local collocation scheme for solutions of first-order systems of lin ear two-point boundary value problems is developed that preserves unif ormly the superconvergent accuracy at meshpoints achieved by collocati on at Gauss points over piecewise polynomials. The method uses the sup erconvergent meshpoint values from the first collocation along with a second collocation that can be done independently on each piece. A com plete mathematical analysis is provided for the special cases when the points for the second collocation are equally spaced, either open or closed. It is shown that the choice of Gauss points for this second co llocation is always undesirable.